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On distributed reduced-order observer-based protocol for linear multiagent consensus under switching topology. (English) Zbl 1271.93033

Summary: We discuss linear multiagent systems consensus problem with distributed reduced-order observer-based protocol under switching topology. We use Jordan’s decomposition method to prove that the proposed protocols can solve consensus problems under directed fixed topology. By constructing a parameter-dependent common Lyapunov function, we prove that the distributed reduced-order observer-based protocol can also solve the continuous-time multi-agent consensus problem under the undirected switching interconnection topology. Then, we investigate the leader-following consensus problem and propose a reduced-order observer-based protocol for each following agent. By using similar analysis method, we can prove that all following agents can track the leader under a class of directed interaction topologies. Finally, the given simulation example also shows the effectiveness of our obtained result.

MSC:

93B07 Observability
03B10 Classical first-order logic
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
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[1] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514 · doi:10.1109/TAC.2003.812781
[2] Vicsek, T.; Czirk, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 75, 6, 1226-1229 (1995) · doi:10.1103/PhysRevLett.75.1226
[3] Corson, N.; Aziz-Alaoui, M. A.; Ghnemat, R.; Balev, S.; Bertelle, C., Modeling the dynamics of complex interaction systems: from morphogenesis to control, International Journal of Bifurcation and Chaos, 22, 2 (2012) · Zbl 1270.37036 · doi:10.1142/S0218127412500253
[4] Ren, W.; Beard, R. W., Distributed Consensus in Multivehicle Cooperative Control: Theory and Applications (2008), Berlin, Germany: Springer, Berlin, Germany · Zbl 1144.93002
[5] Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) · Zbl 1192.93019 · doi:10.1016/j.automatica.2010.03.006
[6] Xiao, F.; Wang, L., Consensus problems for high-dimensional multi-agent systems, IET Control Theory and Applications, 1, 3, 830-837 (2007) · doi:10.1049/iet-cta:20060014
[7] Olfati-Saber, R.; Fax, A. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233 (2007) · Zbl 1376.68138 · doi:10.1109/JPROC.2006.887293
[8] Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182 (2006) · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013
[9] Hu, J.; Hong, Y., Leader-following coordination of multi-agent systems with coupling time delays, Physica A, 374, 2, 853-863 (2007) · doi:10.1016/j.physa.2006.08.015
[10] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control, 53, 6, 1503-1509 (2008) · Zbl 1367.93567 · doi:10.1109/TAC.2008.924961
[11] Lin, P.; Jia, Y., Further results on decentralised coordination in networks of agents with second-order dynamics, IET Control Theory & Applications, 3, 7, 957-970 (2009) · doi:10.1049/iet-cta.2008.0263
[12] Ren, W.; Moore, K. L.; Chen, Y., High-order and model reference consensus algorithms in cooperative control of multivehicle systems, ASME Journal of Dynamic Systems, Measurement, and Control,, 129, 5, 678-688 (2007) · doi:10.1115/1.2764508
[13] Jiang, F.; Wang, L., Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies, International Journal of Control, 83, 2, 404-420 (2010) · Zbl 1184.93008 · doi:10.1080/00207170903177774
[14] Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50, 5, 655-661 (2005) · Zbl 1365.93302 · doi:10.1109/TAC.2005.846556
[15] Hong, Y.; Wang, X., Multi-agent tracking of a high-dimensional active leader with switching topology, Journal of Systems Science & Complexity, 22, 4, 722-731 (2009) · Zbl 1300.93014 · doi:10.1007/s11424-009-9197-z
[16] Gao, L.; Tang, Y.; Chen, W.; Zhang, H., Consensus seeking in multi-agent systems with an active leader and communication delays, Kybernetika, 47, 5, 773-789 (2011) · Zbl 1236.93006
[17] Ni, W.; Cheng, D., Leader-following consensus of multi-agent systems under fixed and switching topologies, Systems & Control Letters, 59, 3-4, 209-217 (2010) · Zbl 1223.93006 · doi:10.1016/j.sysconle.2010.01.006
[18] Gao, L.; Zhang, J.; Chen, W., Second-order consensus for multiagent systems under directed and switching topologies, Mathematical Problems in Engineering, 2012 (2012) · doi:10.1155/2012/273140
[19] Yamapi, R.; Enjieu Kadji, H. G.; Filatrella, G., Stability of the synchronization manifold in nearest neighbor nonidentical van der Pol-like oscillators, Nonlinear Dynamics, 61, 1-2, 275-294 (2010) · Zbl 1204.70016 · doi:10.1007/s11071-009-9648-z
[20] Chen, Y.; Lü, J.; Han, F.; Yu, X., On the cluster consensus of discrete-time multi-agent systems, Systems & Control Letters, 60, 7, 517-523 (2011) · Zbl 1222.93007 · doi:10.1016/j.sysconle.2011.04.009
[21] Zhao, J.; Aziz-Alaoui, M. A.; Bertelle, C., Cluster synchronization analysis of complex dynamical networks by input-to-state stability, Nonlinear Dynamics, 70, 2, 1107-1115 (2012) · Zbl 1268.93089 · doi:10.1007/s11071-012-0516-x
[22] Sun, Y., Mean square consensus for uncertain multiagent systems with noises and delays, Abstract and Applied Analysis, 2012 (2012) · Zbl 1242.93006 · doi:10.1155/2012/621060
[23] Li, H., Observer-type consensus protocol for a class of fractional-order uncertain multiagent systems, Abstract and Applied Analysis, 2012 (2012) · Zbl 1253.93095 · doi:10.1155/2012/672346
[24] Yang, X.-R.; Liu, G.-P., Necessary and sufficient consensus conditions of descriptor multi-agent systems, IEEE Transactions on Circuits and Systems I, 59, 11, 2669-2677 (2012) · Zbl 1468.93043 · doi:10.1109/TCSI.2012.2190663
[25] Sun, F.; Guan, Z.-H.; Zhan, X.-S.; Yuan, F.-S., Consensus of second-order and high-order discrete-time multi-agent systems with random networks, Nonlinear Analysis: Real World Applications, 13, 5, 1979-1990 (2012) · Zbl 1254.93011 · doi:10.1016/j.nonrwa.2011.12.009
[26] Münz, U.; Papachristodoulou, A.; Allgöwer, F., Consensus in multi-agent systems with coupling delays and switching topology, IEEE Transactions on Automatic Cotrol, 56, 12, 2976-2982 (2011) · Zbl 1368.93010 · doi:10.1109/TAC.2011.2161052
[27] Wang, X.; Hong, Y.; Huang, J.; Jiang, Z.-P., A distributed control approach to a robust output regulation problem for multi-agent linear systems, IEEE Transactions on Automatic Control, 55, 12, 2891-2895 (2010) · Zbl 1368.93577 · doi:10.1109/TAC.2010.2076250
[28] Su, Y.; Huang, J., Cooperative output regulation of linear multi-agent systems, IEEE Transactions on Automatic Control, 57, 4, 1062-1066 (2012) · Zbl 1369.93051 · doi:10.1109/TAC.2011.2169618
[29] Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850 (2008) · Zbl 1283.93019 · doi:10.1016/j.automatica.2007.07.004
[30] Gao, L.; Zhu, X.; Chen, W., Leader-following consensus problem with an accelerated motion leadera, International Journal of Control, Automation and Systems, 10, 5, 931-939 (2012) · doi:10.1007/s12555-012-0509-z
[31] Bowong, S.; Yamapi, R., Adaptive observer based synchronization of a class of uncertain chaotic systems, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 18, 8, 2425-2435 (2008) · Zbl 1165.34389 · doi:10.1142/S0218127408021798
[32] Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, IEEE Transactions on Circuits and Systems I, 57, 1, 213-224 (2010) · Zbl 1468.93137 · doi:10.1109/TCSI.2009.2023937
[33] Zhang, H.; Lewis, F. L.; Das, A., Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback, IEEE Transactions on Automatic Control, 56, 8, 1948-1952 (2011) · Zbl 1368.93265 · doi:10.1109/TAC.2011.2139510
[34] Gao, L.; Zhu, X.; Chen, W.; Zhang, H., Leader-following consensus of linear multi-agent systems with state-observer under switching topologies, Mathematical Problems in Engineering, 2013 (2013) · doi:10.1155/2013/873140
[35] Li, Z.; Liu, X.; Lin, P.; Ren, W., Consensus of linear multi-agent systems with reduced-order observer-based protocols, Systems & Control Letters, 60, 7, 510-516 (2011) · Zbl 1222.93013 · doi:10.1016/j.sysconle.2011.04.008
[36] Seo, J. H.; Shim, H.; Back, J., Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach, Automatica, 45, 11, 2659-2664 (2009) · Zbl 1180.93005 · doi:10.1016/j.automatica.2009.07.022
[37] Li, Z.; Duan, Z.; Chen, G., Dynamic consensus of linear multi-agent systems, IET Control Theory & Applications, 5, 1, 19-28 (2011) · doi:10.1049/iet-cta.2009.0466
[38] Dong, W., Distributed observer-based cooperative control of multiple nonholonomic mobile agents, International Journal of Systems Science, 43, 5, 797-808 (2012) · Zbl 1307.93025 · doi:10.1080/00207721.2010.520096
[39] Horn, R. A.; Johnson, C. R., Matrix Analysis (1985), New York, NY, USA: Cambridge University Press, New York, NY, USA · Zbl 0576.15001
[40] Chen, C., Linear System Theory and Design (1999), New York, NY, USA: Oxford University Press, New York, NY, USA
[41] Wonham, W. M., Linear Multivariable Control (1985), New York, NY, USA: Springer, New York, NY, USA · Zbl 0314.93008
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